Quantum Dynamics of Machine Learning
This provides a theoretical foundation for machine learning that could support implementation on quantum computers, though it appears incremental in applying existing quantum concepts to ML.
The authors derived a quantum dynamic equation for machine learning based on the Schrödinger equation, reformulating iterative processes as time-dependent partial differential equations to provide a theoretical framework. They validated this approach by examining fundamental iterative processes, diffusion models, and activation functions like Softmax and Sigmoid.
The quantum dynamic equation (QDE) of machine learning is obtained based on Schrödinger equation and potential energy equivalence relationship. Through Wick rotation, the relationship between quantum dynamics and thermodynamics is also established in this paper. This equation reformulates the iterative process of machine learning into a time-dependent partial differential equation with a clear mathematical structure, offering a theoretical framework for investigating machine learning iterations through quantum and mathematical theories. Within this framework, the fundamental iterative process, the diffusion model, and the Softmax and Sigmoid functions are examined, validating the proposed quantum dynamics equations. This approach not only presents a rigorous theoretical foundation for machine learning but also holds promise for supporting the implementation of machine learning algorithms on quantum computers.